Question

use a trigonometric ratio to solve for z. round to two decimal places as necessary. draw show your work here z =

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 61^{\circ}$, the adjacent side to the $61^{\circ}$ angle is 25 and the hypotenuse is $z$. So, $\cos61^{\circ}=\frac{25}{z}$.

Step2: Solve for $z$

We know that $\cos61^{\circ}\approx0.4848$. Then, $z=\frac{25}{\cos61^{\circ}}$.

Step3: Calculate the value of $z$

$z=\frac{25}{0.4848}\approx51.57$.

Answer:

$z\approx51.57$